The information entropy maximization method was applied by Jou er al. [J. Phys. A 17, 2799 (1984)] to heat conduction in the past. Advancing this method one more step, Nettleton [J. Chem. Phys. 106, 10311 (1997)] combined the method with a projection operator technique to derive a set of evolution equations for macroscopic variables from the Liouville equation for a simple liquid, and a claim was made that the method provides a statistical mechanical theory basis of irreversible processes and, in particular, of extended thermodynamics which is consistent with the laws of thermodynamics. This line of information entropy maximization method is analyzed from the viewpoint of the laws of thermodynamics in this paper.